Just something i am trying to figure out in my head but can't decide on an answer, so thought i'd ask for some help.

The situation is: Hero is in position, and gets to the river HU. Villain checks to hero, and hero now has a betting range of K high and A high flushes. The actual board isn't relevant, but assume A high flush is the nuts, and K high is the 2nd nuts.

Hero bets, and gets checkraised to a size that, in order to be unexploitable, hero would need to defend 50% of his range (pot). Assuming he has equal combos of A and K high flushes, then am i right in thinking he only ever needs to call with A high flushes?

However, if hero is 100% certain that villains raising range will always contain the nut blocker (either as a bluff, or the nut flush), then hero can never have the A high flush. At this point hero's range becomes exclusively K high flushes. Does this mean that hero would have to call with some Kx in order to be unexploitable? I don't have a great knowledge of GT, but i know a lot of you guys do so this may be a really easy question for you. It seems to me that the idea of playing GTO means that it is irrelevant what cards villain holds when he makes a raise, but at the same time seems wrong to be in a spot where hero is folding 100% of his range.

Any thoughts?